Analysis of relativistic effects in GNSS measurements based on calculation of metric tensor components and comparison with existing models

International Journal of Electronics and Telecommunications

“…To take into account the time correction of the synchronization of the satellite's atomic clock and the one of the ground control station, we use the following formula [20]: We choose the following notation: the coordinates are taken in square brackets, in them the reference frame is denoted in parentheses, the superscript indicates the type of the coordinate. For example, a = 0 corresponds to time coordinate ct; a = 1, 2, 3 corresponds to spatial coordinates in the cylindrical coordinate system, R is cylindrical radius, φ is cylindrical longitude, z is axis cylindrical coordinate system respectively; g(8)00, g (8)0α are the components of the metric tensor in the geocentric reference frame {х(8) α } (the four-dimensional metric tensor will be denoted by g; the subscripts indicate a specific component of the tensor, the reference frame for which the given tensor is found is indicated in parentheses, the frames of reference will be taken in curly brackets.…”